The potential difference applied to an X-ray tube is 5k V and the current through it is 3.2 mA. Then, the number of electrons striking the target per second is __________.

Options

A. `2xx 10^(16)`
B. `5 xx 10^(6)`
C. `1 xx 10^(17)`
D. `4 xx 10^(15)`

Explanation

To solve the problem of finding the number of electrons striking the target per second in an X-ray tube, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between current, charge, and time**:
The current (I) in an electrical circuit is defined as the rate of flow of charge (Q) per unit time (t). Mathematically, this can be expressed as:
\[ I = \frac{Q}{t} \]
where \( Q \) is the total charge in coulombs, and \( t \) is the time in seconds.

2. **Relate charge to the number of electrons**:
The total charge \( Q \) can also be expressed in terms of the number of electrons (n) and the charge of a single electron (e):
\[ Q = n \cdot e \]
where \( e \) (the charge of an electron) is approximately \( 1.6 \times 10^{-19} \) coulombs.

3. **Substituting the expressions into the current equation**:
By substituting \( Q \) in the current equation, we get:
\[ I = \frac{n \cdot e}{t} \]
Rearranging this gives:
\[ n = \frac{I \cdot t}{e} \]

4. **Insert the known values**:
We are given:
- Current \( I = 3.2 \, \text{mA} = 3.2 \times 10^{-3} \, \text{A} \)
- Time \( t = 1 \, \text{s} \)
- Charge of an electron \( e = 1.6 \times 10^{-19} \, \text{C} \)

Now substituting these values into the equation for \( n \):
\[ n = \frac{3.2 \times 10^{-3} \, \text{A} \cdot 1 \, \text{s}}{1.6 \times 10^{-19} \, \text{C}} \]

5. **Calculate the number of electrons**:
Performing the calculation:
\[ n = \frac{3.2 \times 10^{-3}}{1.6 \times 10^{-19}} = 2 \times 10^{16} \]

6. **Final answer**:
Therefore, the number of electrons striking the target per second is:
\[ n = 2 \times 10^{16} \text{ electrons} \]